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Math Help - Determining the countability of a set of function.

  1. #1
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    Determining the countability of a set of function.

    Determine whether or not the set D of all functions f:\mathbb{Z}_+\to\mathbb{Z}_+{ is countable. Justify your answer.

    If anyone could give me some hints I could use to get started on this question I would really appreciate it. I have been trying to use the fact that D is a subset of the power set of \mathbb{Z}_+\times\mathbb{Z}_+ but is have not really been able to get anywhere with that.
    Last edited by auitto; October 12th 2010 at 03:02 PM.
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  2. #2
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    The set of all functions f:\mathbb{Z}^+\to \{0,1\}=2^{\mathbb{Z}^+ } which in equipotent to \mathscr{P}\left(\mathbb{Z}^+ \right), the power set of  \mathbb{Z}^+ .

    Is it not true that  \left| {\mathbb{Z}^ +  } \right| < \left| {\mathscr{P}\left( {\mathbb{Z}^ +  } \right)} \right|?
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